1. Field of the Invention
The present invention relates to a feedback control method for a chaos system using adaptive tracking, and more particularly to an improved feedback control method for a chaos system using adaptive tracking that is capable of automatically searching a control condition based on a control bifurcation (CB) phenomenon of a feedback control. The present invention is able to perform feedback control irrespective of variations of a parameter of a chaos system.
2. Description of the Conventional Art
Generally, the chaos characteristic is presented based on a nonlinear characteristic of a dynamics system. The nonlinear dynamics system having the above-mentioned chaos characteristic is called a "chaos system".
The chaos system is provided concurrently and hierarchically with various movements such as a chaos movement, a periodic movement and a fixed point movement, distinguishing it from conventional dynamics systems not having the chaos characteristic. The movements which distinguish a chaos system from conventional dynamics systems can be detected by analyzing the bifurcation phenomenon with respect to variation of the system parameter of the chaos system.
The bifurcation phenomenon is one of the important characteristics of the chaos system. Based on this phenomenon, it is possible to presume that a periodic resolution and a chaos-based resolution concurrently and hierarchically exist in one system.
The bifurcation can be expressed as a function of a certain system parameter. Assuming that the bifurcation is a system bifurcation (SB), this system bifurcation is referred to as a system itself.
Controlling the chaos system is referred to as stabilizing an unstable periodic orbit (UPO), which orbit is provided in the chaos attractor by slightly applying a perturbation to a parameter of the chaos system.
One feedback control method used in industry to stabilize a chaos system is known as the OGY method. The OGY method was disclosed in 1990 by Ott, Grebogy, and Yorke of the University of Maryland in the U.S.A. The OGY method applies a weak feedback perturbation to achieve a system parameter of the chaos system. As such, this feedback control method achieves control using many UPOs which are internally provided in the attractor. That is, the OGY method is evaluated as a theoretical basic principle of the chaos control.
Another feedback control method of the chaos system is known as an occasional proportional feedback (OPF) method disclosed by Hunt in 1991. The OPF method samples one time serial data at a sampling period T and applies a feedback control based on a difference between a sampled data and a reference point when the sampled data is positioned within the previously set control window. The method is easy to use and is adaptable to a high speed system.
Yet another feedback control method used to stabilize chaos systems is a return map method, disclosed by Peng and Pettrov in 1991. The return map method is directed to forming a return map from one-time serial data and performing feedback control to stabilize the UPO. The method is easy to use and has an advantage in using natural period of the system.
However, in the above-mentioned OGY method, various pre-analysis are necessary. That is, a disadvantage of the OGY system is that it requires the attractor to be reformed from the time serial data, the position of the UPOs to be analyzed by checking the data based on the Poincare cross-sectional surface and characteristics of the UPO which are determined in accordance with the variation of the system parameter.
The above-described OPF method, which samples based on a sampling period T, is also problematic in that it requires the period to be set to nearly match the natural period of the system. That is, since the method itself is not systematical, an experiment-based method is necessary.
A disadvantage of the conventional feedback control methods used in the conventional chaos systems is that the answer speed is low since complicated system analyzing processes must be performed with respect to the chaos system before performing the feedback control. The above-mentioned methods are therefore not useful for chaos systems requiring a quick answer time since the answering time is delayed due to the complicated system-analyzing processes.